中国科学院数学与系统科学研究院
数学研究所
学术报告
复动力系统研讨班
Speaker:杨璐鲜 副研究员（深圳大学）
Title: Multicurves and Thurston’s Theorem
Time&Venue: 2024.11.29（周五）9:30-10:30 &腾讯会议：509-228-862
Abstract:Multicurves are a valuable tool in the study of dynamics of rational maps. In this talk, I will introduce basic concepts and known results related to multicurves. Building on these foundations, we will introduce Thurston’s characterization of postcritically finite rational maps.
Title: Dynamics on a Periodic Complementary Component of a Completely Stable Multicurve
Time&Venue: 2024.11.29（周五）10:40-11:40 &腾讯会议：509-228-862
Abstract:Besides characterizing rational maps, completely stable multicurves can be used to decompose their dynamics. In this talk, I will present a theorem which explains the dynamics on a periodic complementary component of a completely stable multicurve and show that the small Julia set is immersed into the original one.
Title:Relationship Between Dynamics on Complementary Components of a Completely stable multicurve
Time&Venue: 2024.12.6（周五）9:30-10:30 &腾讯会议：104-922-083
Abstract:A completely stable multicurve gives a decomposition of a rational map. On each complementary component of the multicurve, we associate a small Julia set. In this talk, we introduce coiling curves and explore the relationship between dynamics on distinct components. In particular, we prove that two small Julia sets are disjoint if and only if they are separated by a coiling curve.
附件：